Today, more and more printing systems are developed for the reproduction of color images. Several printing technologies are used such as conventional photography, electrophotography, thermal transfer, dye sublimation and ink jet systems to name a few.
All these systems can be described as multidimensional color printers with n colorants, such as the CMYK (cyan, magenta, yellow and black) inks of an ink jet system. In this document it is assumed that the colorant values range from 0% (no colorant laid down on the receiving substrate such as paper) to 100% (maximum amount of colorant laid down on the receiving substrate).
With colorant space is meant an n-dimensional space with n the number of independent variables with which the printer can be addressed. In the case of an offset printing press the dimension of the space corresponds to the number of inks of the printer. When CMYK inks are used, the dimension of the colorant space is normally four.
The colorant gamut is defined by the possible combinations of the colorant values, normally ranging from 0% to 100%. If there are no colorant limitations, the colorant gamut is a n-dimensional cube.
With color space is meant a space that represents a number of quantities of an object that characterize its color. In most practical situations, colors will be represented in a 3-dimensional space such as the CIE XYZ space. However, also other characteristics can be used such as multi-spectral values based on filters that are not necessarily based on a linear transformation of the color matching functions to represent color.
A printer model is a mathematical relation that expresses color values as a function of colorants for a given printer. The variables for the colorants are denoted as c1, c2, . . . , cn, with n the dimension of the colorant space. An n-ink process is completely characterized by its colorant gamut with a number of colorant limitations and the printer model. Because of this close relationship between an n-ink process and the printer model, the operations typical for a printer model are also defined for the n-ink process.
The printer model is often based on a printer target. Such a target consists of a number of uniform color patches, defined in the colorant space of the printing device. The printer target is printed and measured, and based on the values of the patches in colorant space and the measured values, the printer model is made. A printer target is normally based on a number of sampling points along the different colorant axes. Based on the sampling points a regular grid can be constructed in colorant space of which a number of grid points are contained by the printer target. Hence a target can be said to be complete or incomplete, see EP-A-1 146 726 herein incorporated by reference in its entirety for background information for complete and incomplete printer targets.
Creating the printer model is also called characterizing the printer; this is an important step in the consistent reproduction of images. Before a printer is characterized, it is first calibrated, i.e. put in a standard state. When the printer model is created, it can be inverted in order to obtain a so-called characterization transformation (or inverse printer model). The characterization transformation transforms given colors from color space (typically CIELAB) to the colorant space of the printing device, whereas the printer model transforms given colorant values in the colorant space of the printer to color values in color space.
The calculation of the correct amounts of colorant for the rendering of color images on a printer is also called the color separation problem. Most of the color separation strategies known in the art comprise the following steps.
In a first step, the relation between the amounts of colorants and the resulting colors on a printer is characterized. This is done by first printing a set of colorant combinations that spans the dynamic range of the printer and measuring the resulting colors. An example of such a set is the ANSI IT8.7/3 reference target.
In a second step this relation is mathematically modeled, to obtain the printer model. The printer model usually consists of some form of an analytical expression that predicts color for a given combination of colorant amounts.
In a third step the printer model is inverted. This is necessary since the color separation problem is involved with finding a set of colorants that renders a given color and not vice versa.
Different types of printer models can be used, ranging from analytical models simulating the printing process, over polynomials approximating the global behavior of the printer, to localized approximations of the printer in the colorant domain.
An important advantage of localized models is that a simple mathematical expression is used to represent the printer behavior. For such an approach, in most cases the colorant cube is divided into cells that are all modeled separately. A disadvantage is that, at boundaries of neighboring cells, the model is not continuous for the first derivative and hence sometimes slope discontinuities in the modeling can be seen.
In characterizing printing devices, in most cases multi-dimensional Look Up Tables (LUT's) are used. A typical example of such a characterization system is represented by the ICC profile format (ICC stands for International Color Consortium). For printers, both the forward and the inverse relation is needed. The forward relation, embodied in the forward LUT, predicts the color values in function of given colorant values, i.e. it represents the printer model. The inverse relation, embodied in the inverse LUT, gives the colorant values required to obtain given color values, i.e. it represents the characterization transformation of the printer.
A LUT is often characterized by a number of sampling points (or sampling values) per axis. Based on these sampling points, usually a regular grid is constructed. However, it is also possible to construct LUT's with non-regular grids. Also in this case the LUT's can be characterized by sampling points per axis but not all combinations of the sampling points of the different axes result in grid points. We refer to previously cited patent application EP-A-1 146 726 for more information on grids, printer models, complete and incomplete printer targets, and related terms, and to patent application EP-A-1 083 739, herein incorporated by reference in its entirety for background information, for more information on calibration, characterization, and other relevant terms.
In known systems, the sampling points of a LUT are chosen at predetermined values, e.g., for sampling points along a colorant axis c, at colorant values c=0%, 25%, 50%, 75% and 100%.
Several printers have, for one or more of the colorants, multi-density inks, i.e. two or more inks that have a different density and a similar hue, e.g. light cyan and heavy cyan. By means of multi-density inks, the apparent visual resolution of the printed images can be increased. Multi-density inks can be used in several ways; however, if the calibration is based on 1-ink processes, the relation between the multi-density inks is fixed. If there is a light and heavy ink for cyan for example, a relation is given that converts a global cyan value to a light and a heavy cyan value. Hence the printer is still considered as a CMYK device, but internally the global ink values can be converted to multi-density ink values. The relation between a global ink value for a particular colorant and the multi-density ink values is given by an ink splitting table, also called ink mixing table.
There is still a need for an improved method for characterizing a printing device.